Your family decides to take a long road trip for the summer. You will be riding in the

car while it moves at a fairly constant rate for eight hours to reach your destination.
Record your answers to the questions about this road trip below.Describe how you know which is which in this situation.

1 answer

Certainly! On a long road trip where you're traveling at a constant rate for eight hours, we can identify a few key components related to speed, distance, and time. Here's how they correspond and how we know which is which:

  1. Distance (d): This is the total length of the trip you are going to travel. It can be expressed in miles (or kilometers). You determine the distance based on the route taken (e.g., a map or GPS providing the total distance).

  2. Speed (s): This refers to the rate at which the vehicle is moving, usually expressed in miles per hour (mph) or kilometers per hour (km/h). The speed can be determined based on the speed limit or the typical speed you plan to maintain during the trip.

  3. Time (t): This is the total duration of the trip, which you know is eight hours.

Relationships between Distance, Speed, and Time

In this situation, the relationship between these three components is defined by the formula:

\[ d = s \times t \]

Where:

  • \( d \) is the distance,
  • \( s \) is the speed,
  • \( t \) is the time.

Example:

For instance, if you plan to travel at an average speed of 60 mph for eight hours:

  • Speed (s) = 60 mph

  • Time (t) = 8 hours

  • Distance (d) can be calculated as:

    \[ d = 60 , \text{mph} \times 8 , \text{hours} = 480 , \text{miles} \]

Summary

  1. Distance (480 miles) - known from a map or GPS.
  2. Speed (60 mph) - average speed planned for travel.
  3. Time (8 hours) - set duration of the trip.

This systematic approach helps distinguish each variable in the trip scenario. Each component is crucial in planning and executing a successful road trip.